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  <div class="section" id="numpy-meshgrid">
<h1>numpy.meshgrid<a class="headerlink" href="#numpy-meshgrid" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.meshgrid">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">meshgrid</code><span class="sig-paren">(</span><em class="sig-param">*xi</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/lib/function_base.py#L4076-L4211"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.meshgrid" title="Permalink to this definition">¶</a></dt>
<dd><p>Return coordinate matrices from coordinate vectors.</p>
<p>Make N-D coordinate arrays for vectorized evaluations of
N-D scalar/vector fields over N-D grids, given
one-dimensional coordinate arrays x1, x2,…, xn.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 1.9: </span>1-D and 0-D cases are allowed.</p>
</div>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>x1, x2,…, xn</strong><span class="classifier">array_like</span></dt><dd><p>1-D arrays representing the coordinates of a grid.</p>
</dd>
<dt><strong>indexing</strong><span class="classifier">{‘xy’, ‘ij’}, optional</span></dt><dd><p>Cartesian (‘xy’, default) or matrix (‘ij’) indexing of output.
See Notes for more details.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.7.0.</span></p>
</div>
</dd>
<dt><strong>sparse</strong><span class="classifier">bool, optional</span></dt><dd><p>If True a sparse grid is returned in order to conserve memory.
Default is False.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.7.0.</span></p>
</div>
</dd>
<dt><strong>copy</strong><span class="classifier">bool, optional</span></dt><dd><p>If False, a view into the original arrays are returned in order to
conserve memory.  Default is True.  Please note that
<code class="docutils literal notranslate"><span class="pre">sparse=False,</span> <span class="pre">copy=False</span></code> will likely return non-contiguous
arrays.  Furthermore, more than one element of a broadcast array
may refer to a single memory location.  If you need to write to the
arrays, make copies first.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.7.0.</span></p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X1, X2,…, XN</strong><span class="classifier">ndarray</span></dt><dd><p>For vectors <em class="xref py py-obj">x1</em>, <em class="xref py py-obj">x2</em>,…, ‘xn’ with lengths <code class="docutils literal notranslate"><span class="pre">Ni=len(xi)</span></code> ,
return <code class="docutils literal notranslate"><span class="pre">(N1,</span> <span class="pre">N2,</span> <span class="pre">N3,...Nn)</span></code> shaped arrays if indexing=’ij’
or <code class="docutils literal notranslate"><span class="pre">(N2,</span> <span class="pre">N1,</span> <span class="pre">N3,...Nn)</span></code> shaped arrays if indexing=’xy’
with the elements of <em class="xref py py-obj">xi</em> repeated to fill the matrix along
the first dimension for <em class="xref py py-obj">x1</em>, the second for <em class="xref py py-obj">x2</em> and so on.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><code class="xref py py-obj docutils literal notranslate"><span class="pre">index_tricks.mgrid</span></code></dt><dd><p>Construct a multi-dimensional “meshgrid” using indexing notation.</p>
</dd>
<dt><code class="xref py py-obj docutils literal notranslate"><span class="pre">index_tricks.ogrid</span></code></dt><dd><p>Construct an open multi-dimensional “meshgrid” using indexing notation.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>This function supports both indexing conventions through the indexing
keyword argument.  Giving the string ‘ij’ returns a meshgrid with
matrix indexing, while ‘xy’ returns a meshgrid with Cartesian indexing.
In the 2-D case with inputs of length M and N, the outputs are of shape
(N, M) for ‘xy’ indexing and (M, N) for ‘ij’ indexing.  In the 3-D case
with inputs of length M, N and P, outputs are of shape (N, M, P) for
‘xy’ indexing and (M, N, P) for ‘ij’ indexing.  The difference is
illustrated by the following code snippet:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">xv</span><span class="p">,</span> <span class="n">yv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">sparse</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">indexing</span><span class="o">=</span><span class="s1">&#39;ij&#39;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">nx</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ny</span><span class="p">):</span>
        <span class="c1"># treat xv[i,j], yv[i,j]</span>

<span class="n">xv</span><span class="p">,</span> <span class="n">yv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">sparse</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">indexing</span><span class="o">=</span><span class="s1">&#39;xy&#39;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">nx</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ny</span><span class="p">):</span>
        <span class="c1"># treat xv[j,i], yv[j,i]</span>
</pre></div>
</div>
<p>In the 1-D and 0-D case, the indexing and sparse keywords have no effect.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">=</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">nx</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">xv</span><span class="p">,</span> <span class="n">yv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">xv</span>
<span class="go">array([[0. , 0.5, 1. ],</span>
<span class="go">       [0. , 0.5, 1. ]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">yv</span>
<span class="go">array([[0.,  0.,  0.],</span>
<span class="go">       [1.,  1.,  1.]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">xv</span><span class="p">,</span> <span class="n">yv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">sparse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># make sparse output arrays</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">xv</span>
<span class="go">array([[0. ,  0.5,  1. ]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">yv</span>
<span class="go">array([[0.],</span>
<span class="go">       [1.]])</span>
</pre></div>
</div>
<p><a class="reference internal" href="#numpy.meshgrid" title="numpy.meshgrid"><code class="xref py py-obj docutils literal notranslate"><span class="pre">meshgrid</span></code></a> is very useful to evaluate functions on a grid.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">sparse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">xx</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">yy</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">xx</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">yy</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">h</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">contourf</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">,</span><span class="n">z</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../_images/numpy-meshgrid-1.png" src="../../_images/numpy-meshgrid-1.png" />
</div>
</dd></dl>

</div>


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